Global forced response analysis of reacting swirling flows*

Swirling jets are canonical flow fields in reacting flow systems. This study considers hydrodynamic global flow response to an imposed forcing function. A bi-global stability analysis is done on DNS and LES base flow data by the means of linearized, incompressible Navier Stokes and continuity equations. The disturbance equations are obtained around the unforced mean flow, which serves as the base state for this study. The unforced bi-global analysis is used to test the linear stability of the base flow before a forced bi-global analysis framework is set up to examine the flow's dominant coherent structures in a paired forcing/response fashion. Locations of coherent structures in the domain are probed to evaluate a point-to-point transfer function in terms of a flow variable and the results are studied as a function of Strouhal number. The numerical methods in this study involve discretization of the linearized disturbance equations, application of cylindrical boundary conditions for the swirling jet domain, and the solutions obtained using Taylor-hood finite elements in COMSOL. Lastly, the implications for extension of this study to a strict, fully-global analysis along with experimental validation are considered.